A multi-demand operating system underlying diverse cognitive tasks

The existence of a multiple-demand cortical system with an adaptive, domain-general, role in cognition has been proposed, but the underlying dynamic mechanisms and their links to cognitive control abilities are poorly understood. Here we use a probabilistic generative Bayesian model of brain circuit dynamics to determine dynamic brain states across multiple cognitive domains, independent datasets, and participant groups, including task fMRI data from Human Connectome Project, Dual Mechanisms of Cognitive Control study and a neurodevelopment study. We discover a shared brain state across seven distinct cognitive tasks and found that the dynamics of this shared brain state predicted cognitive control abilities in each task. Our findings reveal the flexible engagement of dynamic brain processes across multiple cognitive domains and participant groups, and uncover the generative mechanisms underlying the functioning of a domain-general cognitive operating system. Our computational framework opens promising avenues for probing neurocognitive function and dysfunction.


I. Supplementary Methods
A. fMRI datasets HCP datasets N-back working memory task We used the high-load dynamic brain state from the HCP Nback task identified from our previous study 1 , as the reference state for all other cognitive tasks in the present study.The same sample from the previous study was used in the current study.We selected 122 individuals (ages: 22-36 years old, 79 female/43 male) from 500 subjects (HCP Q1-Q6 Data Release) based on the following criteria: (1) range of head motion in any translational and rotational direction less than 1 voxel; (2) average scan-to-scan head motion less than 0.25 mm; (3) performance accuracy greater than 50% in each task block and session; and (4) right handedness.
The HCP N-back working memory task combines the category specific representation task and the n-back working memory task in a single task across two sessions.Participants were presented with blocks of trials that consisted of pictures of faces, places, tools and body parts.Within each session, the 4 different stimulus types were presented in separate blocks.Furthermore, within each session, half of the blocks are 2-back working memory and half are 0back working memory task.In the 2-back working memory task blocks, subjects were requested to determine whether the current stimulus matches the stimulus in two presentations of stimuli prior within the same block.In the 0-back working memory task blocks, subjects were requested to determine whether the current stimulus matches the target that was presented in the beginning of each block (cue).A 2.5 second cue indicated the task type (and target for 0-back task) at the beginning of each block.Each task session contained 8 task blocks (10 trials of 2.5 seconds each, for 25 seconds) and 4 fixation ("rest") blocks (15 seconds).On each trial, the stimulus was presented for 2 seconds, followed by a 0.5 second inter-trial-interval (ITI).
Relational processing (RP) task We selected 90 individuals from the 122 who had also participated in the n-back study 1 .The following criteria were used: (1) complete behavioral and brain imaging data in two different acquisition sessions; (2) range of head motion in any translational and rotational direction less than 1 voxel; (3) average scan-to-scan head motion less than 0.25 mm.
The RP task involved a relational processing task and a control condition.In the relational processing condition, participants were presented two pairs of objects, with one pair at the top of the screen and the other pair at the bottom.Participants were required to determine whether the top pair of objects and the bottom pairs of objects are different in the same dimension or not.For example, the top pair differed in texture and the bottom pair differs in shape.In the control task, there were two objects presented at the top of the screen, one object at the bottom of the screen and a word in the middle to indicate dimension (e.ge."shape" or "texture").Participants were told to judge whether the bottom object matches either of the top objects in that dimension.Each condition had 3 blocks and each block lasts 18 seconds.There were 4 trials in each relational processing block and 5 trials in each control matching block.In the relational condition, the stimuli were presented for 3500 ms, with a 500 ms ITI.In the matching condition, the stimuli were presented for 2800 ms, with a 400 ms ITI.

DMCC dataset
We used the Dual Mechanism of Cognitive Control (DMCC) dataset 2 which contains four different task paradigms for probing cognitive control: (1) AX continued performance task (AxCPT), (2) Cued task switching task (CuedTS), (3) Sternberg working memory task (Sternberg) and (4) Stroop interference task (Stroop).We used data from 50 individuals (19-42 years old, 31F/19M) out of a total of 89 participants in the DMCC dataset based on the following criteria: (1) complete behavioral and brain imaging data; (2) range of head motion in any translational and rotational direction was less than 1 voxel in all the tasks; (3) average scan-toscan head motion was less than 0.25 mm in all the tasks.
AxCPT AxCPT is a continuous performance task which includes 4 different standard (Go) trial types: AX, AY, BX, and BY, and No-Go stimuli.Participants were presented with the letters A or B followed by letters X or Y (or not "X"), comprising AX, AY, BX, and BY pairs.They are asked to respond to the probe ("X") only if it followed the contextual cue ("A").Participants were to make another response to other cue-probe sequences ("A" then "Y," "B" then "X," or "B" then "Y"), each occurring with much lower probability than the target pair ("AX").The proportions of trial types were set to ensure equal frequencies of A-cue and B-cue trials.CuedTS Participants performed a letter-digit task in which they were cued to respond to either the letter or number in target stimuli which consisted of a letter-digit pair (e.g., "D 3", or "1 A").
Based on the cue, participants had to either categorize the letter as a vowel or consonant, or categorize the digit as even or odd depending on the cue.The Cued task switching task consists of sixteen different stimuli (1A, A1, 2A, A2, 1B, B1, 2B, B2, 3E, E3, 4D, D4, 5H, H5, 6I and I6).Each trial began with a 300 ms fixation cue ("+") in the center of the screen.Following the fixation is a 500 ms task cue ("attend number"/"attend letter") presented in red.If the cue said "Attend Number", participants decided if the number is odd or even.If the cue said "Attend Letter", participants decided whether the letter was a consonant or vowel.A 4000 ms CTI followed.In incongruent trials, the two stimuli activated competing cue-dependent responses (e.g."A 3") whereas in congruent trials, the response was cue-independent (e.g."A 2").Within each scanning run, 3 task blocks alternated with 4 resting fixation blocks (30 sec duration); in each task block, the inter-trial interval was varied randomly (across 3 step sizes).

Sternberg task
In this task participants determined whether a probe matches a list of stimuli presented previously.High and low load conditions differed in the number of stimuli that need to be maintained in working memory.The Sternberg working memory task included 4 different memory set list-lengths (5, 6, 7 and 8 items).The full condition included 90 trials.The proportions were 5-item: 40%, 6-item: 10%, 7-item: 20%, 8-item: 30%.The 5-item and 6-item trials denoted low load (LL) trials and the 7-itme and 8-item trials denoted high load (HL) trials.The retention interval was 4 seconds after which a probe was presented.On half the trials the probe matched one of the stimuli presented during the encoding period.

Stroop task
The Stroop Interference task is a color-word task, in which stimuli are words presented in different colored fonts and participants are asked to name the color of the font in which the words are presented.The task included congruent and incongruent trials.In congruent trials, the word name and font color were the same (e.g., the word RED presented in red font).In incongruent trials, the word name and font color were different (e.g. the word RED presented in green).The full condition includes 72 congruent and 144 incongruent trials.

Stanford dataset
Stop-signal task (SST) Forty-five children with ADHD or TD children (9-12 years old, 22F/23M) completed the SST task during MRI scanning.Each participant performed two runs of the SST with 96 trials per run.Participants were instructed to respond as quickly as possible to green arrows (Go Signal) with their right pointer or middle finger based on the direction of the arrow.In 33% of the trials, after a variable delay, the green arrow turned red (Stop Signal), indicating that the participant should cancel their (prepotent) response.The delay between the Go Signal and the Stop Signal, the SSD varied across trials in a step-wise fashion and was adjusted dynamically to individual performance: beginning at 165ms, it decreased by 33ms for a failed stop, and increased by 33ms for a successful stop.

Task performance statistical test
The effect of cognitive control load was tested using paired t-test between AY and AX, BY and BX conditions in the AxCPT; between Incongruent and Congruent conditions in the CuedTS; between high and low load conditions in the Stern; between Incongruent and Congruent conditions in the Stroop; between relational and match conditions in the RP (Supplementary Table S2 and S6).Data met the assumptions of the statistical tests, including normality and equal variances.

B. State space modeling using BSDS BSDS generative model
Here we briefly describe the BSDS model 3 .Let  denote a -dimensional vector of observed fMRI measurements in time  and for subject .Further, let  denote a 1-of- discrete vector of latent state variables of a hidden Markov model (HMM) with elements  , ∀ = 1, … , .Two consecutive time instances are dependent via a first-order Markov chain through an HMM.Specifically, probability distribution of  depends on the state of the previous latent variable represented by the transition probabilities , where  ≡   = 1 | |  , = 1 , and a marginal distribution ( | ) = ∏  represented by a vector of initial probabilities  where  ≡ ( = 1) 4 .Next, we assume that at a given mode of the system given by the latent state  = 1, observed vector  is generated via a state space model in form of Equations 1-2: Line 1 of the model represents a probabilistic factor analysis model 5,6 where  is a  ×  dimensional linear transformation matrix that transforms data to a subspace of lower dimensionality,  < , described using a -dimensional vector of latent space variables  mediated by an overall bias  and a measurement noise  ∼ (,   ).Line 2 represents an autoregressive (AR) process of order  defined on the latent space variables of the factor analysis model 7 . ⃗ is a vector of AR coefficients.  = diag(  ) is a block diagonal isotropic matrix with elements of   = ( , ,  , , … ,  , ) representing latent space variables from the previous  time frames where T indicates the transpose operator. ∼ ( ,  ) models the remaining error term in latent space.An AR process of a first order,  = 1, is defined on the representations of the observations in the latent subspace,  .Variables (  ,  ⃗ ,  ,  ) are global latent variables which are not a function of time .Detailed theoretical derivations are provided in our previous study 3 .

Advantages of BSDS modelling
The BSDS model has the following key advantages over other approaches: First, BSDS does not require arbitrary sliding windows, nor does it impose temporal boundaries associated with predefined task conditions -this is contrast to previous approaches for characterizing dynamic brain connectivity in fMRI data which rely on ad hoc procedures for determining critical parameters, such as the window length and number of brain states, which are known to greatly influence the estimation of dynamic brain states and connectivity 8 .In contrast, BSDS uses a Bayesian framework to automatically regulate model complexity and directly estimates the optimal number of latent states.
Second, BSDS applies HMM to state space variables of the observed fMRI data, resulting in a parsimonious model of generators underlying the observed data.BSDS applies HMM to latent space variables generated by an autoregressive process, resulting in greater robustness in state identification.
Third, BSDS allowed us to uncover brain states and their dynamic spatiotemporal properties, including probability and sequence of state transitions as well as inter-regional functional connectivity associated with each brain state, in an optimal subspace.In our previous study 3 , we demonstrated that BSDS is robust to noisy and abrupt local changes in fMRI, resulting in more accurately identifying brain states and their temporal dynamic properties than conventional data driven approaches.
Finally, a novel aspect of our study is its use a generative model of brain dynamics derived one task to identify similar states in other tasks.Our generative model allows us to investigate the correspondence between brain states across tasks and test the hypothesis that a latent brain state that is optimal for behavioral performance during working memory 3 also occurs in other cognitive tasks, and predicts behavior.

C. Statistical significance in leave one ROI out analysis
To evaluate the statistical significance of leave one ROI out effect, we build a distribution of leave one ROI out effects from all brain states, from which the significance level (p value) for the effect of leave one ROI out in each ROI in the SH state (e.g.SHAxCPT) was obtained.An FDR correction (p<0.05) was applied to correct for multiple comparisons.

D. General linear model analysis of task-related activation
A general linear model (GLM) analysis was used to determine task-related activation in each of seven cognitive control tasks 9 .Six motion parameters were entered as covariates of no interest, and both canonical hemodynamic response function (HRF) and its time-derivative were used to convolve the stimulus function to form task regressors.
AxCPT included seven task regressors: ANG, BNG, AX, AY, BX, BY and error.The contrast of interest is AY versus AX.Task-related activation for each contrast of interest was extracted in each ROI used in the BSDS analysis: bilateral AI, MFG, FEF, IPL and DMPFC, PCC and VMPFC.

E. gPPI analysis of task-related functional connectivity
Seed-based generalized psychophysiological interaction (gPPI) was used to determine taskrelated functional connectivity 10 .Seeds were placed in the bilateral AI, MFG, FEF, IPL and DMPFC, the same ROIs used in the BSDS analysis.The gPPI model consisted of a physiological variable (the raw time series of a seed), multiple psychological variables (hemodynamic response function convolved main effect of condition of interest), and multiple interaction variables (deconvolved raw time series of the seed multiplied by main effect of condition of interest, and then convolved with the hemodynamic response function).Taskrelated connectivity was computed for each ROI and contrast of interest resulting in an 11x11 matrix with each column representing a seed and each row representing a target.

F. Comparison of state space models with conventional GLM and gPPI analyses
In each of the seven cognitive tasks, we examined whether state-space models generated better model fits with the reference n-back working memory task than conventional GLM 9 and gPPI 10 analyses.For state-space models, we assessed the similarity in mean activity and covariance patterns between SHWM and the best matched brain state SHX in each task X using Pearson's correlation.Similarly, in the case of conventional GLM and gPPI analyses, the similarity in activation/deactivation and gPPI connectivity patterns between the n-back working memory task and each of the seven other cognitive control tasks was determined using Pearson's correlation.

G. Canonical correlation analysis and prediction model
To characterize the relation between brain states and behavioral performance in different tasks, we first used canonical correlation analysis (CCA) to investigate multivariate relations between brain state and cognitive performance measures in each task 11,12 .In each cognitive task, the occupancy rates of the latent brain states were the set of X variables and behavioral measures were the set of Y variables.For the AxCPT, behavioral variables included RT in AX, AY, BX and BY trials.For the CuedTS, behavioral variables included accuracy and RT in congruent and incongruent trials.For the Sternberg, behavioral variables included accuracy and RT in highload and low-load trials.For the Stroop, behavioral variables included accuracy and RT in congruent and incongruent trials.For the SST, behavioral variables included stop accuracy, unsuccessful stop RT, stop-signal delay and stop-signal reaction time.CCA was implemented using python scikit-learn package (https://scikitlearn.org/stable/modules/generated/sklearn.cross_decomposition.CCA.html).
A prediction model based on the CCA was examined using leave-one-out cross validation procedure such that one subject's data was used as the test set and the rest of subjects' data were used as the training set.The training set was then used to train a canonical correlation model and weights from the trained model were applied on the test set to generate predicted canonical variables of X and Y in the test set.This produce repeated N times (N is the sample size) such that each subject's data was used exactly once as a test set.The model performance was evaluated using correlation between predicted canonical variables of X and predicted canonical variables of Y across all the subjects.

H. Univariate brain-behavior correlation analysis
We used Pearson's correlation to examine the association between the occupancy rate of brain state and task-specific measures of cognitive control abilities.Individual data points were excluded in the analyses if they were 3 standard deviations or more away from the means.

I. Power analysis
We performed a power analysis based on the state-behavior relationship identified from our previous study 3 .If we set alpha at p=0.05, a sample size of 39 will provide power of 0.8 to detect the effect of interest.

Statistical significance of state matching
Space closeness was significant between SHWM and SHAxCPT (p=0.01) in the AxCPT, between SHWM and SHCuedTS (p=0.01) in the CuedTS, between SHWM and SHStern (p=0.05) in the Sternberg and between SHWM and SHStroop (p=0.01) in the Stroop.Space closeness was also significant between SHWM and SHSST (p=0.01) in the SST.Space closeness was marginally significant between SHWM and SHRP1 (p=0.1) in RP Session 1 and significant between SHWM and SHRP2 (p=0.04) in RP Session 2 (Supplementary Table S13).
Temporal closeness was significant between SHWM and SHAxCPT (p=0.01) in the AxCPT, between SHWM and SHCuedTS (p=0.01) in the CuedTS, between SHWM and SHStern (p=0.01) in the Sternberg task and between SHWM and SHStroop (p=0.01) in the Stroop.Temporal closeness was also significant between SHWM and SHSST (p=0.05) in the SST.Temporal closeness was significant between SHWM and SHRP1 (p=0.01) in RP Session 1 and significant between SHWM and SHRP2 (p=0.01) in the RP Session 2. (Supplementary Table S13).

Statistical significance of MFG role in leave one ROI out analysis
In the AxCPT, CuedTS and Stroop tasks, the left and right middle frontal gyrus (MFG) had a significant impact on state similarity (p<0.05,FDR corrected).In the in the Sternberg task, the left MFG had a significant impact on the state similarity (p<0.05,FDR corrected).In the SST, the left MFG had marginally significant impact on state similarity (p=0.065,FDR corrected).Taken together, across all the tasks, the MFG, encompassing the dorsolateral prefrontal cortex, had the highest impact on state similarity (Supplementary Figure S5), suggesting that this region is the most important and consistent brain region whose dynamic features contribute to a shared high-load brain state across cognitive tasks.

Robustness of state matching with respect to sample size of the N-back task
To examine the robustness of our findings with respect to the sample size used in generating the reference optimal latent brain state SHWM, we leveraged a larger sample (415 subjects) from the HCP 1200 n-back working memory task and repeated the same BSDS analysis to identify the optimal latent brain state SHWM415.Specifically, we applied similar data inclusion criteria as in our previous study with a more lenient behavioral criterion (accuracy > 50%) allowing more subjects to be included.The selection criteria were: (1) range of head motion in any translational and rotational direction less than 1 voxel; (2) average scan-to-scan head motion less than 0.25 mm; (3) performance accuracy per session >50%; (4) criterion ( 1)-( 3) met in both Sessions 1 and 2 separately; (5) right handed subjects, and ( 6) subjects are unrelated.This leads to the final sample size of 415 subjects (29±4 years old, 22-36 years old, 225 F/190 M).
We applied the same data analysis procedures as in our previous sample.We determined the optimal latent brain state in the n-back working memory task by its dominant occupancy rate in the 2-back working memory blocks and its positive correlation with 2-back task accuracy (Supplementary Figure S10).This optimal latent brain state was labeled as SHWM415, to differentiate the optimal latent brain (SHWM) state reported previously 3 .
Next, we used two state-matching algorithms to determine the correspondence between states in each cognitive task and n-back tasks.Noteworthy, here the key question is whether the state matched to the optimal brain state in the n-back working memory task (from HCP 415 subjects) is the same state matched to the optimal brain state in the n-back working memory task reported in our previous study, which is generated using HCP 122 subjects.To facilitate a straightforward comparison, the new brain states from the n-back working memory task (from HCP 415 subjects) were labeled as SXWM415, in particular the optimal brain state was labeled as SHWM415, and the brain states from all the other cognitive control tasks remained the same labels, which are matched to the SHWM.We found that SHAxCPT, SHCuedTS, SHStern, SHStroop, SHSST, SHRP1 and SHRP2 matches to SHWM415 in each corresponding cognitive task and results from two state-matching algorithm are converging (Supplementary Figure S11-13).
In summary, we replicated the key state matching results such that the state matched to SHWM415 is the same state matched to SHWM in each cognitive task (Supplementary Figures S11-S13).Results further demonstrate the robustness and generalizability of our findings.

Robustness of state matching with respect to reference cognitive tasks
To examine the robustness of our findings with respect to the choice of reference cognitive task, we tested state matching using alternative cognitive tasks as reference.
First, we used the HCP RP task as the reference task.The optimal latent brain state in the Relational Processing task was determined by the occupancy rate of the latent brain state and relation to its cognitive control efficiency score (Accuracy/RT) (Supplementary Table S9).This optimal brain state in the RP task was the same state that best match with SHWM, i.e.SHRP.Next, using SHRP as the reference state, we examined whether the state that matched to SHRP was the same state matched to SHWM.To simplify the comparison with original results, the same state labels were used in these analyses.Supplementary Figure S14 shows the state matched to SHRP in each DMCC task.Supplementary Figure S15 shows the state matched to SHRP in the SST.It turns out that, in each cognitive task, the state matched to SHRP was the same state that matched SHWM.Second, we repeated the same analysis using the SST as the reference task.The optimal latent brain state in the SST was determined by the occupancy rate of the latent brain state and correlation with 1/SSRT, the cognitive control performance index of the SST (Supplementary Table S9).The optimal brain state in the SST was the same state that best matched SHWM, i.e.SHSST.Next, using SHSST as the reference state, we examined whether the state matched to SHSST was the same state matched to SHWM.To simplify the comparison with original results, the same state labels were used in these analyses.Supplementary Figure S16 shows the state matched to SHSST in each DMCC task.Supplementary Figure S17 shows the state matched to SHSST in the RP task.Again, it turns out that, in each cognitive task, the state matched to SHSST was the same state that matched SHWM.
In summary, we replicated the key state matching results such that the state matched to the optimal brain state in other reference cognitive tasks was the same state matched to the SHWM.Results further demonstrate the robustness and generalizability of our findings.

Robustness of the main findings with respect to ROI selection
To examine the robustness of the main findings with respect to ROI selection, we conducted additional analysis using ROIs from an independent meta-analysis.We used NeuroSynth with key term "working memory", which produces a meta-analytic brain map of 1091 studies (https://neurosynth.org/).We selected 9 ROIs from the meta-analysis, including bilateral anterior insula, middle frontal gyrus, frontal eye field, intraparietal lobule and right dorsomedial prefrontal cortex, which match the ROIs used in the main analysis.Also, because the meta-analysis did not include deactivated regions, posterior cingulate cortex and ventromedial prefrontal cortex of the DMN in the main analysis were included in the new ROI set (Supplementary Figure S18a) in order to keep the same number of ROIs (N=11) to match dimensionality and the same approximate cognitive systems.We then tested whether the optimal latent brain state in the nback working memory task with ROI derived from the meta-analysis also plays behaviorally significant role in other cognitive tasks.
First, we applied BSDS to probe latent brain dynamics in the HCP n-back working memory task.
Here the same sample of 122 subjects was used in the analysis.BSDS uncovered 4 distinct latent brain state (Supplementary Figure S18b).We determined the optimal latent brain state in the n-back working memory task by its dominant occupancy rate in the 2-back working memory blocks and its positive contribution to accuracy in the 2-back task condition (r=0.38,p<0.001,Supplementary Figure S18d).Here, the optimal latent brain state is labeled as SHMETA, to differentiate the optimal latent brain (SHWM) state reported in our previous study.
Next, we applied BSDS to probe latent brain dynamics in each of the four DMCC cognitive control tasks independently.BSDS uncovered 5 latent brain states in the AxCPT, 6 latent brain states in the CuedTS, 5 latent brain states in the Sternberg and 6 latent brain states in the Stroop.Two state-matching algorithms were used to determine the state that matches SHMETA, which is labeled as SHAxCPT, SHCuedTS, SHStern, SHStroop in each DMCC task, respectively (Supplementary Figure S19).
We then examined whether the latent brain state that matches SHMETA plays an important role in cognitive control in each DMCC task.We conducted the same brain-behavior analyses, including multivariate CCA and univariate Pearson's correlation analysis.CCA revealed significant canonical correlations between occupancy rate (OR) of latent brain states and key behavioral measures in each DMCC task (Supplementary Figure S20a-d).Univariate analysis revealed that OR of SHAxCPT is significantly and positively correlated with cognitive control index in the AxCPT (r=0.29,p=0.04);OR of SHCuedTS is positively correlated with cognitive control index in the CuedTS with marginal significance (r=0.25,p=0.08);OR of SHStern is significantly and positively correlated with cognitive control index in the Sternberg (r=0.37,p=0.007); and OR of SHStroop is significantly and positively correlated with cognitive control index in the Stroop (r=0.28,p=0.04) (Supplementary Figure S20e-h).
Next, we applied BSDS to probe latent brain dynamics in the SST independently.BSDS uncovered 4 latent brain states in the SST.Two state-matching algorithms were used to determine the state that matches SHMETA, which is labeled as SHSST (Supplementary Figure S21).
We then examined whether the latent brain state that matches SHMETA plays an important role in the SST.We conducted the same brain-behavior analyses, including multivariate CCA and univariate Pearson's correlation analysis.CCA revealed significant canonical correlations between OR of latent brain states and key behavioral measures in the SST (Supplementary Figure S22).Univariate analysis revealed that OR of SHSST is significantly and positively correlated with cognitive control index in the SST (r=0.32,p=0.03) (Supplementary Figure S22).
Finally, we applied BSDS on the RP task.In both sessions of the RP task, BSDS uncovered 4 latent brain states.Two state-matching algorithms were used to determine the states that match SHMETA, which are labeled as SHRP1 and SHRP2 in session 1 and 2, respectively (Supplementary Figure S23).
We examined whether the latent brain state that matches SHMETA plays an important role in each session of the RP task.We conducted the same brain-behavior analyses, including multivariate CCA and univariate Pearson's correlation analysis.CCA revealed significant canonical correlations between OR of latent brain states and key behavioral measures in each session of the RP task (Supplementary Figure S24a).Univariate analysis revealed that OR of SHRP1 is significantly and positively correlated with cognitive control index in the session 1 (r=0.25,p=0.02) and OR of SHRP2 is significantly and positively correlated with cognitive control index in the session 2 (r=0.28,p=0.01) (Supplementary Figure S24b).
In summary, we replicated the key results in the main analysis using ROIs derived from the meta-analysis, demonstrating the robustness of our findings with respect to the selection of ROIs.
Supplementary Figure S19.Shared latent brain state across four different dual mode of cognitive control (DMCC) tasks (reference is SHMETA) with ROIs derived from an independent meta-analysis.(a,b) BSDS uncovered 5 dynamic brain states in the AxCPT (N=50).SHAxCPT showed the highest state space closeness (c=1) and highest state temporal closeness (r=0.82) with SHMETA.BSDS uncovered 6 dynamic brain states in the CuedTS task.SHCuedTS showed the moderate state space closeness (c=0.75) and the moderate state temporal closeness (r=0.67) with SHMETA.BSDS uncovered 5 dynamic brain states in the Sternberg working memory task.SHStern showed the highest state space closeness (c=0.96) and the highest state temporal closeness (r=0.6) with SHMETA.BSDS uncovered 6 dynamic brain state in the Stroop task.SHStroop showed the highest state space closeness (c=0.76) and the highest state temporal closeness (r=0.68) with SHMETA.SHMETA refers to the high-load dynamic brain state in the n-back working memory task with ROIs derived from an independent meta-analysis.In each task, the best matched four latent states are illustrated here.Color bars are the scales for state space closeness and state temporal closeness.Supplementary Figure S23.Shared latent brain state across two sessions of the RP task (reference is SHMETA) with ROIs derived from an independent meta-analysis.(a, b) BSDS uncovered 4 dynamic brain states in both Sessions 1 and 2 (N=90).SHRP1 has the highest state space closeness (c=16) and high state temporal closeness (r=0.97) with SHMETA in Session 1. SHRP2 has the highest state space closeness (c=7.2) and high state temporal closeness (r=0.9) with SHMETA in Session 2. SHMETA refers to the high-load dynamic brain state in the n-back working memory task with ROIs derived from an independent meta-analysis.SHRP1 and SHRP2 refers to the dynamic brain states that matches to SHMETA in the Relational task session 1 and 2, respectively.Color bars are the scales for state space closeness and state temporal closeness.S2

Supplementary Table
included three task regressors: Congruent, Incongruent and error.The contrast of interest is Incongruent versus Congruent.Sternberg included three task regressors: Low load, High load and error.The contrast of interest is HL versus LL.Stroop included three task regressors: Congruent, Incongruent and error.The contrast of interest is Incongruent versus Congruent.SST included four task regressors: Go Correct (Go), Go Error, Successful Stop (SuccStop), and Unsuccessful Stop (UnsuccStop).The contrast of interest is SuccStop versus Go.RP sessions 1 and 2 included three task regressors: Match, Relational Processing (Relation) and error.The contrast of interest is Relation versus Match.
. Behavioral results for AxCPT, CuedTS, Sternberg and Stroop tasks in the DMCC study.Con: congruent; Incon = Incongruent.P values were not adjusted for multiple comparisons.Source data are provided as a Source data file.Supplementary TableS6.Behavioral results for the RP task.MC = Matching Control; ACC = Accuracy; RT = Reaction Time.P values were not adjusted for multiple comparisons.Source data are provided as a Source data file.Supplementary TableS8.Summary of brain-behavior relations across tasks.Multivariate relation analysis showed significant canonical correlation between occupancy rates of latent brain states and behavioral performance in each of the seven cognitive control tasks.Univariate relation analysis showed significant Pearson's correlation between occupancy rate of the multidemand latent brain state (e.g.SHAxCPT) and cognitive control index in each cognitive control task.AxCPT: A-x continued performance task; SST: Stop-signal task; RP1/2: Relational Processing session 1/2.P values were not adjusted for multiple comparisons.Supplementary TableS10.OR of latent brain states in relation to indices of cognitive control in each task.In each task, the state that matched SHWM was the only state with significant and positive contribution to the cognitive control index.P values were not adjusted for multiple comparisons.